1. Categorization/Classification
Given:
A description of an instance, x  X, where X is the instance language or instance space.
A fixed set of classes:
C = {c1, c2,…, cJ}
Determine:
The category of x: c(x)C, where c(x) is a classification function whose domain is X and whose range is C.
We want to know how to build classification functions (“classifiers”).

2. More Text Classification Examples: Many search engine functionalities use classification
Assign labels to each document or web-page:
Labels are most often topics such as Yahoo-categories
e.g., "finance," "sports," "news>world>asia>business"
Labels may be opinion on a person/product
e.g., “like”, “hate”, “neutral”
Labels may be domain-specific
e.g., "interesting-to-me" : "not-interesting-to-me”
e.g., “contains adult language” : “doesn’t”

3. Classification Methods
Manual classification
Used by Yahoo! (originally)
Very accurate when job is done by experts
Consistent when the problem size and team is small
Difficult and expensive to scale
Means we need automatic classification methods for big problems 3

4. Classification Methods
Supervised learning of a document-label assignment function
Many systems partly rely on machine learning (MSN, Verity, Yahoo!, …)
k-Nearest Neighbors (simple, powerful)
Naive Bayes (simple, common method)
… plus many other methods
No free lunch: requires hand-classified training data
Note that many commercial systems use a mixture of methods 4

5. Classification—A Two-Step Process
Model construction: describing a set of predetermined classes
Each tuple/sample is assumed to belong to a predefined class, as determined by the class label attribute
The set of tuples used for model construction is training set
The model is represented as classification rules, decision trees, or mathematical formulae

6. Classification—A Two-Step Process
Model usage: for classifying future or unknown objects
Estimate accuracy of the model
The known label of test sample is compared with the classified result from the model
Accuracy rate is the percentage of test set samples that are correctly classified by the model
Test set is independent of training set, otherwise over-fitting will occur
If the accuracy is acceptable, use the model to classify data tuples whose class labels are not known

7. Process (1): Model Construction
Classification
Algorithms
Training
Data
Classifier
(Model)
IF rank = ‘professor’
OR years > 6
THEN tenured = ‘yes’

8. Process (2): Using the Model in Prediction
Classifier
Testing
Data
Unseen Data
(Jeff, Professor, 4)
Tenured?

9. Supervised vs. Unsupervised Learning
Supervised learning (classification)
Supervision: The training data (observations, measurements, etc.) are accompanied by labels indicating the class of the observations
New data is classified based on the training set
Unsupervised learning (clustering)
The class labels of training data is unknown
Given a set of measurements, observations, etc. with the aim of establishing the existence of classes or clusters in the data

10. The goal of the course
Study supervised learning specially for text and hypertext documents
Text
Has a very large number of potential features, of which many are irrelevant.
If vector space model is used, each term is a potential feature.
The number of distinct class labels is much larger than structured leaning scenarios.

11. Topics including in the course
Evaluating text classifiers
Classifiers
NN learners
Bayesian learners
Hypertext classification
Feature selection methods

12. Evaluating text classifiers
Accuracy
The ability to predict the correct class labels
This is based on comparing the classifier-assigned labels with human-assigned labels
Speed
time to construct the model (training time)
time to use the model (classification/prediction time)
Simplicity, speed, and scalability for document insertion, deletion and modification
Scalability: efficiency in disk-resident databases
Interpretability
understanding and insight provided by the model

13. Benchmarks Reuters 20NG WebKB Labeled documents : 10700
Number of terms : 30000
Number of categories : 135
20NG
Labeled documents : 18800
Number of terms : 94000
Number of categories : 20
WebKB
Labeled documents : 8300
Number of categories : 7

14. Measures of accuracy
Each document is associated with a subset of classes
To avoid searching over the power set of class labels, many systems create a two-class problem for every class
Two-way ensemble or one-vs.-rest technique
Ensemble classifiers are evaluated on the basis of recall and precision

15. Classifier Accuracy Measures
(guess)~C1 C1
(true)
~C1
True negative
False positive
False negative
True positive
Classifier Accuracy Measures

16. A combined measure: F
Combined measure that assesses precision/recall tradeoff is F measure (weighted harmonic mean):
People usually use balanced F1 measure
i.e., with  = 1 or  = ½ ( b2 = (1-a)/a )

17. F: Example
precision?
recall?
F1?

18. F: Why harmonic mean?
The simple (arithmetic) mean is 50% for “return-everything” search engine, which is too high.
Desideratum: Punish really bad performance on either precision or recall.
Taking the minimum achieves this.
But minimum is not smooth and hard to weight.
F (harmonic mean) is a kind of smooth minimum.

19. Nearest Neighbor Learner
Basic idea
Similar documents are expected to be assigned the same class label.
Vector space model and cosine measure for similarity let us formalize the idea.

20. The k-Nearest Neighbor Algorithm
All instances correspond to points in the n-D space
The nearest neighbor are defined in terms of cosine similarity
k-NN returns the most common value among the k training examples nearest to xq
Vonoroi diagram: the decision surface induced by 1-NN for a typical set of training examples . _ _ . _ _ + . . + . _ xq + . _ +

21. Discussion on the k-NN Algorithm
Distance-weighted nearest neighbor algorithm
Weight the contribution of each of the k neighbors according to their distance to the query xq
Give greater weight to closer neighbors
Robust to noisy data by averaging k-nearest neighbors
Curse of dimensionality: distance between neighbors could be dominated by irrelevant attributes
To overcome it, elimination of the least relevant attributes

22. Bayesian Methods
Learning and classification methods based on probability theory.
Bayes theorem plays a critical role in probabilistic learning and classification.
Build a generative model that approximates how data is produced
Uses prior probability of each category given no information about an item.
Categorization produces a posterior probability distribution over the possible categories given a description of an item.

23. Bayes’ Rule

24. Naive Bayes Classifiers
Task: Classify a new instance D based on a tuple of attribute values into one of the classes cj  C

25. Naïve Bayes Assumption
P(cj)
Can be estimated from the frequency of classes in the training examples.
P(x1,x2,…,xn|cj)
O(|X|n•|C|) parameters
Could only be estimated if a very, very large number of training examples was available.
Naïve Bayes Conditional Independence Assumption:
Assume that the probability of observing the conjunction of attributes is equal to the product of the individual probabilities P(xi|cj).

26. The Naïve Bayes Classifier
Flu X1 X2 X5 X3 X4
fever
sinus
cough
runnynose
muscle-ache
Conditional Independence Assumption: features detect term presence and are independent of each other given the class:
This model is appropriate for binary variables
Multivariate Bernoulli model

27. Learning the Model First attempt: maximum likelihood estimatesC X1 X2 X5 X3 X4 X6
First attempt: maximum likelihood estimates
simply use the frequencies in the data

28. Naïve Bayesian Classifier: Training Dataset
C1:buys_computer = ‘yes’
C2:buys_computer = ‘no’
Data sample
X = (age <=30,
Income = medium,
Student = yes
Credit_rating = Fair)

29. An Example P(Ci): P(buys_computer = “yes”) = 9/14 = 0.643
P(buys_computer = “no”) = 5/14= 0.357
Compute P(X|Ci) for each class
P(age = “<=30” | buys_computer = “yes”) = 2/9 = 0.222
P(age = “<= 30” | buys_computer = “no”) = 3/5 = 0.6
P(income = “medium” | buys_computer = “yes”) = 4/9 = 0.444
P(income = “medium” | buys_computer = “no”) = 2/5 = 0.4
P(student = “yes” | buys_computer = “yes) = 6/9 = 0.667
P(student = “yes” | buys_computer = “no”) = 1/5 = 0.2
P(credit_rating = “fair” | buys_computer = “yes”) = 6/9 = 0.667
P(credit_rating = “fair” | buys_computer = “no”) = 2/5 = 0.4
X = (age <= 30 , income = medium, student = yes, credit_rating = fair)
P(X|Ci) : P(X|buys_computer = “yes”) = x x x = 0.044
P(X|buys_computer = “no”) = 0.6 x 0.4 x 0.2 x 0.4 = 0.019
P(X|Ci)*P(Ci) : P(X|buys_computer = “yes”) * P(buys_computer = “yes”) = 0.028
P(X|buys_computer = “no”) * P(buys_computer = “no”) = 0.007
Therefore, X belongs to class (“buys_computer = yes”)

30. Problem with Max Likelihood
Flu X1 X2 X5 X3 X4
fever
sinus
cough
runnynose
muscle-ache
What if we have seen no training cases where patient had no flu and muscle aches?
Zero probabilities cannot be conditioned away, no matter the other evidence!

31. Smoothing to Avoid Overfitting
The estimate is 0 because of sparseness
The training data are never large enough to represent the frequency of rare events adequately
To eliminate zeros, we use add-one or Laplace smoothing
# of terms in the vocabulary

32. Underflow Prevention: log space
Multiplying lots of probabilities, which are between 0 and 1 by definition, can result in floating-point underflow.
Since log(xy) = log(x) + log(y), it is better to perform all computations by summing logs of probabilities rather than multiplying probabilities.
Class with highest final un-normalized log probability score is still the most probable.

33. Two Models Model 1: Multivariate Bernoulli
One feature Xw for each word in dictionary
Xw = true in document d if w appears in d
Naive Bayes assumption:
Given the document’s topic, appearance of one word in the document tells us nothing about chances that another word appears

34. Example

35. Text classification example(multivariate Bernoulli model)

36. Two Models Model 2: Multinomial = Class conditional unigram
One feature Xi for each word pos in document
feature’s values are all words in dictionary
Value of Xi is the word in position i
Naïve Bayes assumption:
Given the document’s topic, word in one position in the document tells us nothing about words in other positions
Second assumption:
Word appearance does not depend on position
for all positions i,j, word w, and class c

37. Parameter estimation Multivariate Bernoulli model: Multinomial model:
Can create a mega-document for topic j by concatenating all documents in this topic
Use frequency of w in mega-document
fraction of documents of topic cj
in which word w appears
fraction of times in which
word w appears
across all documents of topic cj

38. Naïve Bayes: Learning From training corpus, extract Vocabulary
Calculate required P(cj) and P(xk | cj) terms
For each cj in C do
docsj  subset of documents for which the target class is cj
Textj  single document containing all docsj
for each word xk in Vocabulary
nk  number of occurrences of xk in Textj

39. Naïve Bayes: Classifying
positions  all word positions in current document which contain tokens found in Vocabulary
Return cNB, where

40. Text classification example(multinomial model)
P(c)=3/4, P(~c)=1/4
P(chinese|c)=(5+1)/(8+6)=3/7
P(Tokyo|c)=P(Japan|c)=(0+1)/(8+6)=1/14
P(chinese|~c)=(1+1)/(3+6)=2/9
P(tokyo|~c)=p(Japan|~c)=(1+1)/(3+6)=2/9 d5
c : (3/4)*(3/7)3*(1/14)*(1/14)=0.0003
~c:(1/4)*(2/9)3*(2/9)*(2/9)=0.0001

41. Stochastic Language Models
Models probability of generating strings (each word in turn) in the language (commonly all strings over ∑). E.g., unigram model
Model M
0.2 the
0.1 a
0.01 man
0.01 woman
0.03 said
0.02 likes …
the
man
likes
the
woman
0.2
0.01
0.02
0.2
0.01
multiply
P(s | M) =

42. Stochastic Language Models
Model probability of generating any string
Model M1
Model M2
0.2 the
class
0.03 sayst
0.02 pleaseth
0.1 yon
0.01 maiden
woman
0.2 the
0.01 class
sayst
pleaseth
yon
maiden
0.01 woman
maiden
class
pleaseth
yon
the
0.0005
0.01
0.0001
0.2
0.02
0.1
P(s|M2) > P(s|M1)

43. Unigram and higher-order models
Unigram Language Models
Bigram (generally, n-gram) Language Models
P ( )
= P ( )
P ( | )
P ( | )
P ( | )
Easy.
Effective!
P ( ) P ( ) P ( ) P ( )
P ( ) P ( | ) P ( | ) P ( | )

44. WebKB Experiment (1998) Classify webpages from CS departments into:
student, faculty, course,project
Train on ~5,000 hand-labeled web pages
Cornell, Washington, U.Texas, Wisconsin
Crawl and classify a new site (CMU)
Results: 44

45. NB Model Comparison: WebKB

46. Classification Multinomial vs Multivariate Bernoulli
Multinomial model is almost always more effective in text applications!

47. Naive Bayes is Not So Naive
Naïve Bayes: First and Second place in KDD-CUP 97 competition, among 16 (then) state of the art algorithms
Goal: Financial services industry direct mail response prediction model: Predict if the recipient of mail will actually respond to the advertisement – 750,000 records.
Robust to Irrelevant Features
Irrelevant Features cancel each other without affecting results
Instead Decision Trees can heavily suffer from this.
Very good in domains with many equally important features
Decision Trees suffer from fragmentation in such cases – especially if little data
A good dependable baseline for text classification (but not the best)!
Optimal if the Independence Assumptions hold: If assumed independence is correct, then it is the Bayes Optimal Classifier for problem
Very Fast: Learning with one pass of counting over the data; testing linear in the number of attributes, and document collection size
Low Storage requirements

48. Hypertext classification
Search engines assign heuristic weights to terms that occur in specific HTML tags
Paying special attention to tags can help with supervised learning as well

49. Hypertext classification
It is important to distinguish between the two occurrences of the word “surfing”
resume.publication.title.surfing
resume.hobbies.item.surfing
Relations provide a uniform way to codify hypertextual features.
Ex: contains-text(resume.hobbies.item, wind-surfing)
Ex: links-to(source, destination)

50. Rule Induction

51. Rule Induction
The outer loop learns new rules one at a time, removing positive examples covered by any rule generated thus far.
When a new empty rule is initialized, its free variables can be bound in all possible ways
The inner loop adds conjunctive literals to the new rule until no negative example is covered by the new rule.
A heuristic is to pick a literal that rapidly increases the ratio of surviving positive to negative bindings.

52. Feature Selection: Why?
Text collections have a large number of features
10,000 – 1,000,000 unique words … and more
May make using a particular classifier feasible
Some classifiers can’t deal with 100,000 of features
Reduces training time
Training time for some methods is quadratic or worse in the number of features
Can improve generalization (performance)
Eliminates noise features
Avoids overfitting 52

53. Feature selection: how?
An easy one
Ignoring terms that are “too frequent” or “too rare” according to empirically chosen threshold.
General idea:
Hypothesis testing statistics:
Are we confident that the value of one categorical variable is associated with the value of another
Chi-square test

54. 2 statistic (CHI)
2 is interested in (fo – fe)2/fe summed over all table entries: is the observed number what you’d expect given the marginals?
The null hypothesis is rejected with confidence .999, since 12.9 > (the value for .999 confidence).
9500
500
(4.75)
(0.25)
(9498) 3
Class  auto
(502) 2
Class = auto
Term  jaguar
Term = jaguar
expected: fe
observed: fo 54

55. 2 statistic (CHI) There is a simpler formula for 2x2 2:
D = #(¬t, ¬c)
B = #(t,¬c)
C = #(¬t,c)
A = #(t,c)
N = A + B + C + D 55

56. Feature Selection Chi-square Statistical foundation
May select very slightly informative frequent terms that are not very useful for classification